I'm afraid I don't have any useful thoughts. It's just a file. The log I've been keeping since October of 2014 has about 19,000 lines in it now and is just short of a megabyte. Gzip takes it down to 200K. So it's a pretty easy file to move about.

The whole point is to ignore the log file itself, though, in daily use. I wouldn't want to be porting it around on a thumb drive every day. That being said, you can override the default location with the --directory option. Maybe this plus an alias so you don't have to type the whole path in every time.

Maybe I've misunderstood your question.

How about plain old Git for backups. The files are text files so git works great.